Hill had 12 of his points on four straight 3-pointers as the Vandals (10-16) of the Western Athletic Conference took control of the game with a 16-5 run.
Idaho only had one basket over the final 5:27 but connected on 12 of 13 free throws.
The win was Idaho's first in Pocatello since 1996. The Vandals will rejoin the Big Sky Conference in 2014 for basketball and all sports but football, where they will be independent.
The game was part of the BracketBusters series, but the 101st between the schools.
Nicholls State has hired former Clemson assistant coach Richie Riley as their new men's basketball coach.
Ed Cooley and the Friars added one of the last remaining ESPN 100 prospects in Diallo.
Kory Holden, the No. 2 available transfer in ESPN's rankings after averaging 17.7 points last season for Delaware, is transferring to South Carolina.